Complex geodesics in convex tube domains

• Sylwester Zajac ^[1]
  1. [1] Jagiellonian University

     Jagiellonian University

     Kraków, Polonia

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 14, Nº 4, 2015, págs. 1337-1361
• Idioma: inglés
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• Resumen

  • We describe all the complex geodesics in convex tube domains. In the case where the base of a convex tube domain does not contain any real line, the obtained description involves the notion of boundary measure of a holomorphic map and it is expressed in the language of real Borel measures on the unit circle.

    Applying our result, we calculate all complex geodesics in convex tube domains with unbounded base covering a special class of Reinhardt domains.